Norm-compatible systems of Galois cohomology classes for \(GSp_6\)

We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group \(GSp_6\) compatible when one varies the level at \(p\). These classes are expected constituents of an Euler system for the Galois representations appearing in these cohomology group...

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Bibliographic Details
Published in:arXiv.org 2018-07
Main Authors: Cauchi, Antonio, Joaquín Rodrigues Jacinto
Format: Article
Language:English
Subjects:
Homology
Representations
Online Access:Get full text
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Summary:We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group \(GSp_6\) compatible when one varies the level at \(p\). These classes are expected constituents of an Euler system for the Galois representations appearing in these cohomology groups. As an application, we show how these classes provide elements in the Iwasawa cohomology of these representations and, by applying Perrin-Riou's machinery, \(p\)-adic L-functions associated to them.
ISSN:2331-8422